JSFiddle - React, Tailwind, and code Playground
HTML
<form name="reg_form" method="post" action="ins_data.php">
<table width="530" border="1">
<tr>
<td class="text"><p>Логин:</p></td>
<td class="inputs"><input type="text" id="login_field" name="login_field"/></td>
<td><div class="message" id="login_message"></div></td>
</tr>
</table>
</form>
JavaScript
var login_field = document.getElementById('login_field');
login_field.oninput = function()
{
document.getElementById('login_message').innerHTML = "Проверка!!!";
}